We investigate the influence of an external magnetic field on chiral symmetry breaking in a four-fermion interaction model at finite temperature and chemical potential. Using the Fock-Schwinger proper time method, we calculate the effective potential for the four-fermion interaction model to leading order in the 1/Nc expansion. The phase structure of the chiral symmetry breaking is determined in the T -µ, H-T and µ-H planes. The external magnetic field modifies the phase structure. It is found that a new phase appears for a large chemical

We investigate the influence of an external magnetic field on chiral symmetry breaking in the Nambu-Jona-Lasinio (NJL) model at finite temperature and chemical potential. According to the Fock-Schwinger proper-time method, we calculate the effective potential in the leading order of the 1/N c expansion. The phase boundary dividing the symmetric phase and the broken phase is illustrated numerically. A complex behavior of the phase boundary is found for large chemical potential.

We investigate scalar and spinor field theories in a constant magnetic field at finite temperature and chemical potential. In an external constant magnetic field the exact solution of the two-point Green functions are obtained by using the Fock–Schwinger proper-time formalism. We extend it to the thermal field theory and find the expressions of the Green functions exactly for the temperature, the chemical potential and the magnetic field. For practical calculations the contour of the proper-time integral is carefully selected. The physical contour is discussed in a constant magnetic field at finite temperature and chemical potential. As an example, behavior of the vacuum self-energy is numerically evaluated for the free scalar and spinor fields.

We assess the feasibility of probing dark energy with strong gravitational lensing systems. The capability of the method, which depends on the accuracy with which the lensing systems are modeled, is quantitatively investigated using the Fisher-matrix formalism. We show that this method might place useful constraints on the density parameter and the redshift evolution of the dark energy by combining it with a constraint from supernova measurements. For this purpose, the lens potential needs to be precisely reconstructed. We determine the required quality of data. We also briefly discuss the optimal strategy to constrain the cosmological parameters using gravitational lensing systems.

Motivated by a recent work by Terashima (Phys. Rev. D60 084001), we revisit the fluctuation-dissipation (FD) relation between the dissipative coefficient of a detector and the vacuum noise of fields in curved spacetime. In an explicit